Question

The term independent of $x$ in ${(x^2-\frac{1}{x})}^9$ is

• A. $1$
• B. $-1$
• C. $48$
• D. $84$

Answer 1

Answer: (D)

$84$

We know, $T_{r+1}={}^n{C}_r{a}^{n-r}{b}^r$
Applying to the above question, we get
$T_{r+1}=(-1){}^r{}^9{C}_r{x}^{18-2r}{x}^{-r}$
$=(-1){}^r{}^9{C}_r{x}^{18-3r}$ ...(i)
For term independent of $x$
$18-3r=0$
$\therefore r=6$
Substituting in (i), we get
$T_7={}^9{C}_6$ $=84$